Hi guys, i get stuck with this question. Pls help. thanks so much. I know there are 4 atoms in FCC.
A gold particle was measured to be spherical in shape with a radius of 400 nm. Note that assuming the gold atoms are small spheres that form the gold particle by packing together in a Face-Centered Cubic (FCC) structure. Determine the volume of each gold atom. Note that here A = Angstrom.
To determine the volume of each gold atom in a face-centered cubic (FCC) structure, we can use the formula:
Volume of each atom = Volume of gold particle / Number of atoms
To calculate the volume of the gold particle, we need to use the formula for the volume of a sphere:
Volume of sphere = (4/3) * π * r^3
Where:
- r is the radius of the sphere (given as 400 nm)
Now, let's calculate the volume of the gold particle:
Volume of gold particle = (4/3) * π * (400 nm)^3
Since the given radius is in nanometers (nm), we need to convert the volume to cubic angstroms (ų). The conversion factor for length is 1 nm = 10 Å.
So, the volume of the gold particle in ų becomes:
Volume of gold particle = (4/3) * π * (400 nm * 10 Å/nm)^3
Now, we need to determine the number of atoms in an FCC structure. In an FCC structure, there are 4 atoms per unit cell.
Therefore, the number of atoms = 4
Finally, we can calculate the volume of each gold atom:
Volume of each atom = Volume of gold particle / Number of atoms
Substituting the values we have calculated, we can find the answer.